Efficient computation of Hamiltonian matrix elements between non-orthogonal Slater determinants

TL;DR

This paper introduces a fast numerical method for calculating Hamiltonian matrix elements between non-orthogonal Slater determinants, significantly improving computational efficiency by leveraging matrix-matrix multiplication on modern microprocessors.

Contribution

The paper presents a novel method that transforms sparse array computations into dense matrix multiplications, achieving up to 80% of peak performance and outperforming traditional methods.

Findings

Achieves ~80% of theoretical peak performance on modern microprocessors.

Outperforms traditional sparse array methods by a factor of 5-10.

Demonstrates efficiency gains through optimized memory access strategies.

Abstract

We present an efficient numerical method for computing Hamiltonian matrix elements between non-orthogonal Slater determinants, focusing on the most time-consuming component of the calculation that involves a sparse array. In the usual case where many matrix elements should be calculated, this computation can be transformed into a multiplication of dense matrices. It is demonstrated that the present method based on the matrix-matrix multiplication attains $\sim$80% of the theoretical peak performance measured on systems equipped with modern microprocessors, a factor of 5-10 better than the normal method using indirectly indexed arrays to treat a sparse array. The reason for such different performances is discussed from the viewpoint of memory access.